High critical temperature superconducting (HTS) films have important applications in, e.g., microwave, electronic and optical devices. Presently, however, useful applications for HTS films are limited by the relatively low critical temperatures that have been achieved by conventional HTS film growth. Devices comprising conventional HTS films must be cooled to the films' low operating temperatures using, e.g., a Stirling cycle refrigerator or a Gifford-McMahon-type cryocooler. Currently, typical refrigerators of this type have mean times between failure (MTBFs) of about 4,000 hours, the most reliable models having MTFBs of 150,000 hours, or about 17.5 years. Drawbacks of these refrigerators are that they are expensive and are much less reliable than desired.
Increasing the critical temperature, Tc, of HTS films to 160 K or above would allow them to be cooled inexpensively and reliably. As a result, the use of HTS films could become more widespread. Cooling to 160 K could be provided by highly reliable solid state thermoelectric coolers that operate based on the Seebeck effect. MTFBs of 200,000 to 300,000 hours (34 years) are commonplace among such thermoelectric coolers. Furthermore, these devices are inexpensive, widely used and readily available. Another benefit that would be realized from being able to use thermoelectric coolers is that the power required to cool an. HTS device having a Tc greater than 160 K would be relatively small compared to a conventionally cooled HTS device. Therefore, operating costs of thermoelectrically cooled HTS devices would be lower.
As reported in the CRC Handbook of Chemistry and Physics, 80th Edition, pp. 12-91 to 12-92, CRC Press LLC (1999), the present record for the highest Tc of an HTS film is 133 K, which is held by a mercury-based copper oxide superconducting compound. Critical temperatures of other HTS materials may also be found in the foregoing reference. In Gao et al., “Superconductivity up to 164 K in HgBaCaCuO under quasi-hydrostatic pressures,” Physical Review B, Vol. 50, pp. 4260-63, The American Physical Society (1994), it was reported that the Tc of the subject compound can be increased to 164 K by applying 300,000 atmospheres of hydrostatic pressure to it. This hydrostatic pressure effect has also been observed in other superconducting compounds, including the lanthanum, bismuth and thalium compounds, and to a lesser degree in yttrium compounds. While these increases are of scientific interest, they are not suitable for practical applications.
Recently, J. Loquet et al. reported in “Doubling the critical temperature of LaSrCuO using epitaxial strain,” Nature, Vol. 394, 1998, pp. 453-56, that greater increases in Tc can be achieved by inducing compressive strain into the a-b plane of the HTS film by growing the HTS film pseudomorphically on a substrate having a lattice constant smaller than the lattice constant of the bulk HTS material, rather than by applying hydrostatic pressure. To achieve the relatively large increases in Tc that are desirable for allowing the use of less expensive and more reliable cooling apparatus, a relatively large lattice mismatch between the HTS film and the substrate is required.
However, such a large lattice mismatch causes problems in growing a high quality, low defect HTS film. For example, a large lattice mismatch increases the energy of formation required for the lattice structure of the HTS film to conform to the lattice structure of the substrate. This increase in energy increases the likelihood that defects, such as dislocations, will occur in the HTS film during its growth. Such defects can degrade the superconducting properties of the HTS film and decrease the strain in the film. Therefore, it is desirable to grow an HTS film at the lowest energy of formation as possible to achieve the highest quality film.
Conventional pseudomorphic epitaxy, however, cannot achieve the desired low energy of formation and thus places severe limitations on the thickness of an HTS film having its Tc increased via a lattice mismatch between the substrate and HTS film. As the magnitude of the lattice mismatch increases, the maximum thickness to which a high quality film can be grown decreases. The lattice mismatch induces strain into the HTS film within only about the first few hundred angstroms of thickness adjacent the substrate. Beyond these first few hundred angstroms, the strain in the HTS film caused by the lattice mismatch is significantly diminished due to dislocations. These limitations on HTS film thickness may not be compatible with a desired application. For example, in some applications, such as microwave filters and current fault limiters, among others, it is desired that the thickness of the HTS film be on the order of 1000 Å or more. It is, therefore, desirable to induce the Tc raising strains into an HTS film after it has been grown at the lowest energy of formation possible so that the problems of pseudomorphic epitaxy are avoided.
Belenky et al. have reported, in “Effect of stress along the ab plane on the Jc and Tc of YBa2Cu307 thin films,” Physical Review B, Vol. 44, No. 10, pp. 10, 117-120, The American Physical Society (1991), that the Tc of a thin YBa2Cu3O7 film grown on a substrate to form a composite structure can be changed from the unstrained Tc by bending the composite structure to induce a stress into the HTS film. For their experiment, one end of the composite structure was clamped into a fixed support such that a portion of the composite structure was cantilevered from the fixed support. Then, external forces were alternatingly applied to the composite structure adjacent the free end of the cantilevered portion in a direction normal to the HTS film to alternatingly induce compression and tension into the a-b plane of the HTS film. Belenky et al. found that inducing compression along the a-b plane leads to an increase in Tc above the unstrained Tc, and, conversely, that inducing tension along the a-b plane leads to a decrease in Tc below the unstrained Tc. While these results are of experimental interest, the temporary strains induced into the HTS film are of no value to practical HTS film devices.
In order to facilitate an understanding of the present invention, following is a presentation of orientation conventions, terminology, equations and empirical data used in the present specification and/or claims appended hereto. It is noted that Equations {1}-{8} appearing below are generally valid only for relatively small magnitudes of strain, i.e., where the relationship between strain and Tc is generally linear. These equations may not adequately describe the relationship between strain and Tc, for larger magnitudes of strain, wherein the relationship between strain and Tc may be non-linear. Thus, Equations {1}-{8} are presented only to illustrate the general concepts embodied in the various aspects of the present invention.
FIG. 1A shows the relative orientation of the a, b and c directions/axes and a-b plane with respect to a unit 20 of simple cubic crystal lattice structure, and FIG. 1B shows the relative orientation of the a, b and c directional axes and a-b plane of an HTS film 22 grown on a substrate 24. FIGS. 2A and 2B illustrate, respectively, HTS film 22 epitaxially grown commensurate with respect to substrate 24 and, in the alternative, epitaxially grown pseudomorphic with respect to substrate 24. HTS film 22 in FIG. 2A is denoted a commensurate film, characterized in that the b-direction lattice constant Ksb of substrate 32 is equal to the bulk b-direction lattice constant of the HTS material from which HTS film 22 is formed. Thus, when HTS film 22 is grown, its in situ lattice constant Kfb is equal to lattice constant Ksb of substrate 24 so that no strain is induced in HTS film 22 by a lattice mismatch. Since there is no strain in the b-direction, there is no strain in the c-direction base d upon the Poisson effect and, therefore, c-direction lattice constant Kfc of HTS film 22 remains unchanged from its bulk value.
In contrast, HTS film 22 in FIG. 2B is denoted a pseudomorphic film due to the fact that its in situ b-direction lattice constant K′fb is different from its bulk value due the HTS film being grown on a substrate having a b-direction lattice constant K′sb different from the bulk b-direction lattice constant of the HTS material used to form HTS film 22. As HTS film 22 is grown, the lattice structure of HTS film 22 generally conforms to the smaller lattice structure of substrate 24. The decrease in b-direction lattice constant K′f b of HTS film from its bulk, or unstrained, value induces a compressive strain into the HTS film in the a-b plane. Due to the Poisson effect, and since HTS film 22 is unconstrained in the c-direction, the compressive strain in the a-b plane causes the c-direction lattice constant K′hc to increase over its bulk value, thus inducing a corresponding tensile strain in the HTS film in the c-direction direction.
For many of the copper superconducting compounds it is known that the Tc rises for compressive stress in the a-b plane and falls for compressive stress in the c-direction. Under hydrostatic pressure, the HTS film is under compressive stress in both the a-b plane and c direction, and, thus, any increase in Tc due to the compressive stress in the a-b plane tends to be canceled by the decrease caused by the compressive stress in the c direction. However, as described above, for pseudomorphic HTS film grown epitaxially on a substrate having a lattice constant smaller than the lattice constant of the unstained HTS film, the a-b plane is under compressive (positive) strain and the c plane is under a tensile (negative) strain. Thus, under pseudomorphic conditions, the changes in Tc of the aforementioned copper oxide compounds are additive to one another and lead to a larger increase in TC when compared to a hydrostatic pressure scenario. Similarly, with respect to lanthanum-based superconducting compounds, inducing a compressive strain in the a-b plane and a corresponding tensile strain in the c direction has been observed to double the Tc.
The strain within an HTS thin film grown epitaxially on a substrate is given by the equation:εa=dB−dSub/dB  1 where εa is the strain in the a-direction, dB is the lattice constant of the bulk superconducting material and dSub is the lattice constant of the substrate in the a-direction. The strain in the b-direction can be obtained using the same formula and replacing the a-direction lattice constants of the respective material with the corresponding b-direction lattice constants. For many superconducting materials, the a-direction and b-direction lattice constants are nearly the same. As stated above, strain in the a-b plane also gives rise to strain in the c-direction due to the Poisson effect. Thus, the strain in the c-direction is given by the equation:εc=−2σεa  2 where εc is the strain in the c-direction, σ is Poisson's ratio for HTS material and εa is the strain in the a-direction. Note that the strain in the c-direction has the opposite sign of the strain in the a (or b)direction.
The critical temperature, Tc, of an HTS film as a function of epitaxial strain is given by the equation:Tc=Tc(0)+(δTc/δεa)εa+(δTc/δεb)εa+(δTc/δεc)εc  3 where Tc(0) is the critical temperature of the HTS material in the absence of strain, δTc/δεx is the derivative of the critical temperature with respect to the strain in the x-direction, εx is the strain in the x-direction and the subscripts a, b, c refer to the respective x-direction.
The stress in an epitaxial HTS film is related to the strain by Hooke's law and the Poisson effect as shown in the following equation:ΔPa=Y εa/(1−σ)  4 where ΔPa is the stress in the a-direction, Y is Young's modulus of the HTS material, εa is the strain in the a-direction and σ is Poisson's ratio. The stress in the b-direction uses the same equation except the subscripts are changed to b to indicate that the corresponding terms are for the b-direction. The stress in the c-direction is given by the equation:ΔPc=Yεa/(−2σ)  5 where ΔPc is the stress in the c-direction and e, is the corresponding strain in the a-direction. It is noted that the stress in the c-direction has the opposite sign of the stress in each the a and b-directions.
The critical temperature, Tc, of a HTS thin film as a function of stress is given by the equation:Tc=Tc(0)+(δTc/δPa)ΔPa+(δTc/δPb)ΔPb+(δTc/δPc)ΔPc  6 where Tc(0) is the critical temperature of the HTS film in the absence of stress, δTc/δPx is the derivative of the critical temperature with respect to the stress in the x-direction, ΔPx is the stress in the x-direction and the subscripts a, b, c refer to the respective x-direction.
The expected increase in critical temperature per unit stress, ΔTce, for epitaxial stress in the a-b plane is given by the equation:ΔTce=2dTc/dPab−dTc/dPc  7 where dTc/dPab and dTc/dPc are the derivatives of the critical temperature with respect to the stress in the a-b plane and the stress in the c-direction, respectively. In contradistinction, however, the expected increase in critical temperature per unit stress, ΔTch, for the hydrostatic pressure case is given by the equation:ΔTch=2dTc/dPab+dTc/dPc  8 where the terms are the same as for the epitaxial strain case. It is significantly noted that the signs of the operators preceding the term of each of Equations {7} and {8} are opposite one another.
The Tc derivatives with respect to strain and the expected increases in critical temperature for each of the hydrostatic pressure and epitaxial strain cases are listed in TABLE 1 for several bismuth copper oxide HTS materials. TABLE 1 indicates that large increases in critical temperature are expected for films under compressive epitaxial strain. Furthermore, these expected increases are much larger than the expected increases under hydrostatic pressure.
dTc/dPabdTc/dPcMaterial(K/Gpa)(K/GPa)ΔTch (K/GPa)ΔTce (K/GPa)BiSrCaCuO-1.8−2.8+0.86.42212Bi(Pb)SrCaCuO-10−18.5+1.538.52212Bi(Pb)SrCaCuO-6.2−18.5−6.130.92223
For most copper oxide HTS materials, the derivative of the critical temperature with respect to pressure is positive in the a and b-directions and negative in the c-direction. When an epitaxial HTS film is grown under compressive strain, the film in the a and b-directions is under compressive strain and the film in the c-direction is under tensile strain. Thus, for most HTS films grown under compressive strain in the a and b-direction, the a and b-direction derivatives and strains are positive and the c-direction derivative and strain are negative. Therefore, the a, b and c derivatives constructively add with one another to increase the critical temperature of the HTS film. Conversely, an epitaxial HTS film grown under tensile strains in the a and b-directions would experience a commensurate decrease in critical temperature. In contradistinction, when HTS film is subject to hydrostatic pressure in the c-direction, the Tc derivative term in the c-direction tends to cancel the Tc derivative terms in the a and b-directions, reducing the magnitude of the change in critical temperature.